1. Warm-Up Exercises SOLUTION EXAMPLE 1 Use the SSS Similarity Theorem Compare ABC and DEF by finding ratios of corresponding side lengths. Shortest sides AB DE 4 3 8 6 == Is either DEF or GHJ similar to ABC ?

2. Warm-Up Exercises EXAMPLE 1 Longest sides CA FD 4 3 16 12 == Remaining sides BC EF 4 3 12 9 = = Shortest sides Use the SSS Similarity Theorem AB GH 8 8 == 1 All of the ratios are equal, so ABC ~ DEF. ANSWER Compare ABC and GHJ by finding ratios of corresponding side lengths.

3. Warm-Up Exercises EXAMPLE 1 Use the SSS Similarity Theorem Longest sides CA JG 16 == 1 Remaining sides BC HJ 6 5 12 10 = = The ratios are not all equal, so ABC and GHJ are not similar. ANSWER

4. Warm-Up Exercises SOLUTION EXAMPLE 2 Use the SSS Similarity Theorem ALGEBRA Find the value of x that makes ABC ~ DEF. STEP 1Find the value of x that makes corresponding side lengths proportional. 4 12 = x –1 18 Write proportion.

5. Warm-Up Exercises EXAMPLE 2 Use the SSS Similarity Theorem 4 18 = 12(x – 1) 72 = 12x – 12 7 = x Cross Products Property Simplify. Solve for x. Check that the side lengths are proportional when x = 7. STEP 2 BC = x – 1 = 6 6 18 4 12 = AB DE BC EF = ?

6. Warm-Up Exercises EXAMPLE 2 Use the SSS Similarity Theorem DF = 3(x + 1) = 24 8 24 4 12 = AB DE AC DF = ? When x = 7, the triangles are similar by the SSS Similarity Theorem. ANSWER

7. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 1. Which of the three triangles are similar? Write a similarity statement. MLN ~ ZYX. ANSWER

8. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 2. The shortest side of a triangle similar to RST is 12 units long. Find the other side lengths of the triangle. ANSWER 15, 16.5

9. Warm-Up Exercises EXAMPLE 3 Use the SAS Similarity Theorem Lean-to Shelter You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown?

10. Warm-Up Exercises EXAMPLE 3 Use the SAS Similarity Theorem Both m A and m F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F. ~ SOLUTION Shorter sidesLonger sides AB FG 3 2 9 6 == AC FH 3 2 15 10 == The lengths of the sides that include A and F are proportional.

11. Warm-Up Exercises EXAMPLE 3 Use the SAS Similarity Theorem ANSWER So, by the SAS Similarity Theorem, ABC ~ FGH. Yes, you can make the right end similar to the left end of the shelter.

12. Warm-Up Exercises EXAMPLE 4 Choose a method Tell what method you would use to show that the triangles are similar. Find the ratios of the lengths of the corresponding sides. Shorter sidesLonger sides SOLUTION CA CD 3 5 18 30 == BC EC 3 5 9 15 == The corresponding side lengths are proportional. The included angles ACB and DCE are congruent because they are vertical angles. So, ACB ~ DCE by the SAS Similarity Theorem.

13. Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 3. SRT ~ PNQ Explain how to show that the indicated triangles are similar. ANSWER R  N and = =, therefore the triangles are similar by the SAS Similarity Theorem. SR PN RT NQ 4 3

14. Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 4. XZW ~ YZX Explain how to show that the indicated triangles are similar. XZ YZ WZ XZ 4 3 = WX XY = = WZX  XZY and therefore the triangles are similar by either SSS or SAS Similarity Theorems. ANSWER

15. Warm-Up Exercises Daily Homework Quiz 1. Verify that ABC ~ DEF for the given information. ABC : AC = 6, AB = 9, BC = 12; DEF : DF = 2, DE= 3, EF = 4 ANSWER AC DF AB DE BC EF 3 1 = = = so ABC ~ DEF by the SSS Similarity Theorem.. The ratios are equal,

16. Warm-Up Exercises Daily Homework Quiz 2. Show that the triangles are similar and write a similarity statement. Explain your reasoning. ANSWER XY AB YZ BC 3 4 == and Y B. So XYZ ~ ABC = by the SAS Similarity Theorem.